Spectral theory of corrugated surfaces
Jakšić, Vojkan
Journées équations aux dérivées partielles, (2001), p. 1-11 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

We discuss spectral and scattering theory of the discrete laplacian limited to a half-space. The interesting properties of such operators stem from the imposed boundary condition and are related to certain phenomena in surface physics.

@article{JEDP_2001____A8_0,
     author = {Jak\v si\'c, Vojkan},
     title = {Spectral theory of corrugated surfaces},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {2001},
     pages = {1-11},
     doi = {10.5802/jedp.592},
     mrnumber = {1843409},
     zbl = {1029.39021},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_2001____A8_0}
}

Jakšić, Vojkan. Spectral theory of corrugated surfaces. Journées équations aux dérivées partielles,  (2001), pp. 1-11. doi : 10.5802/jedp.592. http://gdmltest.u-ga.fr/item/JEDP_2001____A8_0/

[A] Aizenman M Localization at Weak Disorder: Some Elementary Bounds Rev. Math. Phys., 6, 1163 1994. | MR 1301371 | Zbl 0843.47039

[AM] Aizenman M., Molchanov S Localization at Large Disorder and at Extreme Energies: An Elementary Derivation Commun. Math. Phys. 157, 245 1993. | MR 1244867 | Zbl 0782.60044

[BBP] Bentosela F., Briet Ph., Pastur L, In preparation.

[CS] Chahrour A. Sahbani J, On the Spectral and Scattering Theory of the Schrödinger Operator with Surface Potential Rev. Math. Phys. 12, 561 (2000). | MR 1763841 | Zbl 1044.81034

[CFKS] Cycon H., Froese R., Kirsch W., Simon B., Schrödinger Operators. Springer-Verlag Berlin-Heidelberg 1987. | MR 883643 | Zbl 0619.47005

[G] Grinshpun V Localization for Random Potentials Supported on a Subspace Lett. Math. Phys. 34, 103 1995. | MR 1335579 | Zbl 0831.47052

[GJMS] Gordon Y., Jakšić, V., Molchanov S., Simon B. Spectral Properties of Random Schrödinger Operators with Unbounded Potentials Commun. Math. Phys. 157, 23 1993. | MR 1244857 | Zbl 0788.60077

[DJ] Derezinski J., Jakšić, V Spectral Theory of Pauli-Fierz Hamiltonians J. Funct. Anal. 180, 243 (2001). | MR 1814991 | Zbl 1034.81016

[DS] Davies E.B., Simon B Scattering Theory for Systems with Different Spatial Asymptotics on the Left and Right Commun. Math. Phys. 63, 277 1978. | MR 513906 | Zbl 0393.34015

[FP] Figotin A., Pastur L An Exactly Solvable Model of Multidimensional Incommensurate Structure Commun. Math. Phys. 95, 410 1984. | MR 767188 | Zbl 0582.35101

[JL1] Jakšić, V.,Last Y Corrugated Surfaces and A.C. Spectrum Rev. Math. Phys. 12, 1465 (2000). | MR 1809458 | Zbl 0979.60050

[JL2] Jakšić, V., Last Y, Spectral Structure of Anderson Type Hamiltonians Invent. Math. 141, 561 (2000). | MR 1779620 | Zbl 0962.60056

[JL3] Jakšić, V., Last Y, Surface States and Spectra Commun. Math. Phys. 218, 459 (2001). | MR 1828849 | Zbl 01631803

[JM1] Jakšić, V., Molchanov S, On the Spectrum of the Surface Maryland Model Lett. Math. Phys. 45, 185 1998. | MR 1641176 | Zbl 0916.47027

[JM2] Jakšić, V., Molchanov S, On the Surface Spectrum in Dimension Two Helv. Phys. Acta 71, 629 1999. | MR 1669046 | Zbl 0939.60074

[JM3] Jakšić, V., Molchanov S, Localization of Surface Spectra Commun. Math. Phys. 208, 153 1999. | MR 1729882 | Zbl 0952.60059

[JM4] Jakšić, V., Molchanov S, Wave Operators for the Surface Maryland Model J. Math. Phys. 41, 4452 (2000). | MR 1765613 | Zbl 0983.82007

[JMP] Jakšić, V., Molchanov S., Pastur L., On the Propagation Properties of Surface Waves Wave Propagation in Complex Media, IMA Vol. Math. Appl. 96, 143 1998. | MR 1489748 | Zbl 0905.65107

[KMP] Kirch W., Molchanov S., Pastur L One-dimensional Schrödinger Operator with Unbounded Potential Func. Anal. Prilozhen. 24, 14 1990. | MR 1082027 | Zbl 0747.47023

[KP] Khoruzenko B.A. Pastur L, The Localization of Surface States: An Exactly Solvable Model Physics Reports 288, 109-126 1997. | Zbl 1001.82526

[M1] Molchanov S., Lectures given at Caltech, Spring 1990.

[M2] Molchanov S. Lectures on Random Media. In Lectures on Probability ed. P. Bernard, Lecture Notes in Mathematics, 1581, Springer-Verlag, Heidelberg 1994. | MR 1307415 | Zbl 0814.60093

[MV1] Molchanov S., Vainberg B, unpublished.

[MV2] Molchanov S., Vainberg B private communication.

[SW] Simon B., Wolff T Singular Continuous Spectrum Under Rank One Perturbations and Localization for Random Hamiltonians Commun. Pure Appl. Math. 39, 75 1986. | MR 820340 | Zbl 0609.47001